Due to the congestion in urban rail transit during peak hours, this study proposes a hierarchical coordinated passenger inflow control model for overloaded metro lines from three dimensions, namely line, station and ticket gate. The hierarchical structure divides the system into three control layers and the model is established using the linear programming method. An improved particle swarm optimisation (PSO) algorithm, combining the interior penalty function and the basic PSO algorithm, is used to find the optimal objective value. In addition, the objective function with the penalty function to transform the constrained optimisation problem into an unconstrained optimisation problem is developed to solve the model. Finally, a real-world instance with operation data of the Beijing Metro Line 5 is implemented to demonstrate the performance and effectiveness of the proposed approaches.

中文翻译：

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具有分层协调功能的乘客超载控制地铁线路

由于高峰时段城市轨道交通的拥堵，本研究针对超载地铁线路，从线路，车站和检票口三个维度提出了一种分层协调的客流控制模型。分层结构将系统分为三个控制层，并使用线性编程方法建立模型。结合内部惩罚函数和基本粒子群优化算法，提出了一种改进的粒子群优化算法，以求出最优目标值。此外，还开发了带有惩罚函数的目标函数，将约束优化问题转换为无约束优化问题，以求解模型。最后，